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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mpbarrett.c,v 1.8 2001/06/16 13:00:20 mdw Exp $ |
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4 | * |
5 | * Barrett modular reduction |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: mpbarrett.c,v $ |
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33 | * Revision 1.8 2001/06/16 13:00:20 mdw |
34 | * Use the generic exponentiation functions. |
35 | * |
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36 | * Revision 1.7 2001/04/19 18:25:26 mdw |
37 | * Use sliding-window exponentiation. |
38 | * |
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39 | * Revision 1.6 2000/10/08 12:03:44 mdw |
40 | * (mpbarrett_reduce): Cope with negative numbers. |
41 | * |
419d33ed |
42 | * Revision 1.5 2000/07/29 17:04:33 mdw |
43 | * Change to use left-to-right bitwise exponentiation. This will improve |
44 | * performance when the base is small. |
45 | * |
d34decd2 |
46 | * Revision 1.4 2000/06/17 11:45:09 mdw |
47 | * Major memory management overhaul. Added arena support. Use the secure |
48 | * arena for secret integers. Replace and improve the MP management macros |
49 | * (e.g., replace MP_MODIFY by MP_DEST). |
50 | * |
0a5d0bc7 |
51 | * Revision 1.3 1999/12/12 15:08:52 mdw |
52 | * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least |
53 | * significant digits. |
54 | * |
ed6d1bd2 |
55 | * Revision 1.2 1999/12/11 01:50:56 mdw |
56 | * Improve initialization slightly. |
57 | * |
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58 | * Revision 1.1 1999/12/10 23:21:59 mdw |
59 | * Barrett reduction support: works with even moduli. |
60 | * |
61 | */ |
62 | |
63 | /*----- Header files ------------------------------------------------------*/ |
64 | |
65 | #include "mp.h" |
66 | #include "mpbarrett.h" |
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67 | #include "mpbarrett-exp.h" |
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68 | |
69 | /*----- Main code ---------------------------------------------------------*/ |
70 | |
71 | /* --- @mpbarrett_create@ --- * |
72 | * |
73 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
74 | * @mp *m@ = modulus to work to |
75 | * |
76 | * |
77 | * Returns: --- |
78 | * |
79 | * Use: Initializes a Barrett reduction context ready for use. |
80 | */ |
81 | |
82 | void mpbarrett_create(mpbarrett *mb, mp *m) |
83 | { |
84 | mp *b; |
85 | |
86 | /* --- Validate the arguments --- */ |
87 | |
88 | assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0)); |
89 | |
90 | /* --- Compute %$\mu$% --- */ |
91 | |
92 | mp_shrink(m); |
93 | mb->k = MP_LEN(m); |
94 | mb->m = MP_COPY(m); |
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95 | b = mp_new(2 * mb->k + 1, 0); |
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96 | MPX_ZERO(b->v, b->vl - 1); |
97 | b->vl[-1] = 1; |
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98 | mp_div(&b, 0, b, m); |
99 | mb->mu = b; |
100 | } |
101 | |
102 | /* --- @mpbarrett_destroy@ --- * |
103 | * |
104 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
105 | * |
106 | * Returns: --- |
107 | * |
108 | * Use: Destroys a Barrett reduction context releasing any resources |
109 | * claimed. |
110 | */ |
111 | |
112 | void mpbarrett_destroy(mpbarrett *mb) |
113 | { |
114 | mp_drop(mb->m); |
115 | mp_drop(mb->mu); |
116 | } |
117 | |
118 | /* --- @mpbarrett_reduce@ --- * |
119 | * |
120 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
121 | * @mp *d@ = destination for result |
122 | * @mp *m@ = number to reduce |
123 | * |
124 | * Returns: The residue of @m@ modulo the number in the reduction |
125 | * context. |
126 | * |
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127 | * Use: Performs an efficient modular reduction. |
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128 | */ |
129 | |
130 | mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m) |
131 | { |
132 | mp *q; |
133 | size_t k = mb->k; |
134 | |
135 | /* --- Special case if @m@ is too small --- */ |
136 | |
137 | if (MP_LEN(m) < k) { |
138 | m = MP_COPY(m); |
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139 | if (d) |
140 | MP_DROP(d); |
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141 | return (m); |
142 | } |
143 | |
144 | /* --- First stage --- */ |
145 | |
146 | { |
147 | mp qq; |
148 | mp_build(&qq, m->v + (k - 1), m->vl); |
149 | q = mp_mul(MP_NEW, &qq, mb->mu); |
0a5d0bc7 |
150 | if (MP_LEN(q) <= k) { |
151 | m = MP_COPY(m); |
d34decd2 |
152 | if (d) |
153 | MP_DROP(d); |
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154 | return (m); |
155 | } |
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156 | } |
157 | |
158 | /* --- Second stage --- */ |
159 | |
160 | { |
161 | mp *r; |
162 | mpw *mvl; |
163 | |
164 | MP_COPY(m); |
165 | if (MP_LEN(m) <= k + 1) |
166 | mvl = m->vl; |
167 | else |
168 | mvl = m->v + k + 1; |
d34decd2 |
169 | r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN); |
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170 | mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl); |
d34decd2 |
171 | MP_DEST(d, k + 1, r->f); |
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172 | mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl); |
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173 | d->f = (m->f | r->f) & (MP_BURN | MP_NEG); |
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174 | MP_DROP(r); |
175 | MP_DROP(q); |
176 | MP_DROP(m); |
177 | } |
178 | |
179 | /* --- Final stage --- */ |
180 | |
181 | MP_SHRINK(d); |
182 | while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl)) |
183 | mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl); |
184 | |
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185 | /* --- Fix up the sign --- */ |
186 | |
187 | if (d->f & MP_NEG) { |
188 | mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl); |
189 | d->f &= ~MP_NEG; |
190 | } |
191 | |
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192 | MP_SHRINK(d); |
193 | return (d); |
194 | } |
195 | |
196 | /* --- @mpbarrett_exp@ --- * |
197 | * |
198 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
199 | * @mp *d@ = fake destination |
200 | * @mp *a@ = base |
201 | * @mp *e@ = exponent |
202 | * |
203 | * Returns: Result, %$a^e \bmod m$%. |
204 | */ |
205 | |
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206 | mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e) |
207 | { |
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208 | mp *x = MP_ONE; |
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209 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
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210 | |
211 | MP_SHRINK(e); |
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212 | if (!MP_LEN(e)) |
213 | ; |
214 | else if (MP_LEN(e) < EXP_THRESH) |
215 | EXP_SIMPLE(x, a, e); |
216 | else |
217 | EXP_WINDOW(x, a, e); |
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218 | mp_drop(d); |
219 | mp_drop(spare); |
220 | return (x); |
221 | } |
222 | |
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223 | /*----- Test rig ----------------------------------------------------------*/ |
224 | |
225 | #ifdef TEST_RIG |
226 | |
227 | static int vmod(dstr *v) |
228 | { |
229 | mp *x = *(mp **)v[0].buf; |
230 | mp *n = *(mp **)v[1].buf; |
231 | mp *r = *(mp **)v[2].buf; |
232 | mp *s; |
233 | mpbarrett mb; |
234 | int ok = 1; |
235 | |
236 | mpbarrett_create(&mb, n); |
237 | s = mpbarrett_reduce(&mb, MP_NEW, x); |
238 | |
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239 | if (!MP_EQ(s, r)) { |
21a7c4b1 |
240 | fputs("\n*** barrett reduction failure\n", stderr); |
241 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
242 | fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr); |
243 | fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr); |
244 | fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr); |
245 | ok = 0; |
246 | } |
247 | |
248 | mpbarrett_destroy(&mb); |
249 | mp_drop(x); |
250 | mp_drop(n); |
251 | mp_drop(r); |
252 | mp_drop(s); |
253 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
254 | return (ok); |
255 | } |
256 | |
257 | static int vexp(dstr *v) |
258 | { |
259 | mp *m = *(mp **)v[0].buf; |
260 | mp *a = *(mp **)v[1].buf; |
261 | mp *b = *(mp **)v[2].buf; |
262 | mp *r = *(mp **)v[3].buf; |
263 | mp *mr; |
264 | int ok = 1; |
265 | |
266 | mpbarrett mb; |
267 | mpbarrett_create(&mb, m); |
268 | |
269 | mr = mpbarrett_exp(&mb, MP_NEW, a, b); |
270 | |
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271 | if (!MP_EQ(mr, r)) { |
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272 | fputs("\n*** barrett modexp failed", stderr); |
273 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
274 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
275 | fputs("\n e = ", stderr); mp_writefile(b, stderr, 10); |
276 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
277 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
278 | fputc('\n', stderr); |
279 | ok = 0; |
280 | } |
281 | |
282 | mp_drop(m); |
283 | mp_drop(a); |
284 | mp_drop(b); |
285 | mp_drop(r); |
286 | mp_drop(mr); |
287 | mpbarrett_destroy(&mb); |
288 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
289 | return ok; |
290 | } |
291 | |
292 | static test_chunk tests[] = { |
293 | { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } }, |
294 | { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
295 | { 0, 0, { 0 } } |
296 | }; |
297 | |
298 | int main(int argc, char *argv[]) |
299 | { |
300 | sub_init(); |
301 | test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett"); |
302 | return (0); |
303 | } |
304 | |
305 | #endif |
306 | |
307 | /*----- That's all, folks -------------------------------------------------*/ |